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Subharmonic solutions and Morse theory. (English) Zbl 0605.58015

The aim of this note is to apply Morse-index theory in order to find subharmonic solutions of a forced oscillation problem.

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
58E20 Harmonic maps, etc.

Citations:

Zbl 0516.58017
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References:

[1] Arnold, VI, Mathematical Methods of Classical Mechanics (1978), Springer, (Appendix 9)
[2] Arnold, VI, (Proceedings of Symposia in Pure Mathematics, Vol. XXVIII (1976), A.M.S), 66
[3] Chaperon, M., Quelques questions de géometrie symplectique, (Séminaire Bourbaki (1982-1983)), 610
[4] Conley, CC; Zehnder, E., Isolated invariant sets and the Morse index, (CBMS, Regional Conf. Series in Math., 38 (1978))
[5] Conley, CC; Zehnder, E., The Birkhoff-Lewis fixed point theorem and a conjecture of V I Arnold, Invent. Math., 73, 33-49 (1983) · Zbl 0516.58017
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